---
title: "Control of Gene Expression"
book: "University Biology — Year 1"
subject: biology
language: en
chapter: 20
exercises: 12
source: https://one-course.com/books/biology/3/en/chapter/20-control-of-gene-expression
---

# Chapter 20 — Control of Gene Expression

A bacterium growing on glucose carries five molecules of the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) that digests lactose; give it lactose and, within minutes, it carries five thousand. A liver [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and a [neuron](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-nervous) carry the same twenty thousand [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) and make almost entirely different sets of [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide), and neither will ever make the other’s. Nothing in [Chapter 19](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#ch-b1-gene-expression) explains this: the machinery of expression is the same for every [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene). What differs is whether a [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) is read, how often, and for how long — decisions taken at the promoter by [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) that bind [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain), and after it by the fate of the messenger and the [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide). This chapter describes how bacteria switch [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) on and off in response to their food, how eukaryotes control their [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) through chromatin, distant [enhancers](#def-b1-expression-control-enhancer) and combinations of factors, and how the same control, applied to different [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) in different [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell), makes a body out of one [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome).

## 20.1 Why and where genes are controlled

**Proposition 20.1 (Expression is regulated, at every level).**

Some [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) are *constitutive* — expressed always, at a steady level, because their products are always needed (the [ribosome](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#def-b1-gene-expression-ribosome)’s [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide), the [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) of [glycolysis](https://one-course.com/books/biology/3/en/chapter/15-cellular-respiration-and-fermentation#def-b1-respiration-fermentation-glycolysis)). Most are *regulated*: expressed only in some conditions, some [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell), some moments. The control acts at every step of the flow — chiefly at the start of transcription, the cheapest place to decide, but also at the processing, export, stability and translation of the messenger, and at the modification and degradation of the [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) — and the response times range from seconds (a [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) modified) through minutes (a bacterial [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) switched on) to days (a chromatin state changed).

**Example 20.2 (Making enzymes only when needed).**

The [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) $\beta$-galactosidase, which splits lactose, is a tetramer of four chains of $1024\,$ residues: five thousand copies are $3\,\%$ of a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) and cost $8 \times 10^{7}\,$ [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) per generation. A bacterium that made them with no lactose to digest would grow about one percent slower than a competitor that did not, and in a few hundred generations would be outnumbered. Regulation is selected because expression is expensive.

## 20.2 The lac operon

**Definition 20.3 (Operon, repressor, operator).**

An *operon* is a group of bacterial [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) transcribed together from one promoter into one messenger, and so controlled together. The *lac operon* of *E. coli* comprises three [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) for the use of lactose — *lacZ* ($\beta$-galactosidase), *lacY* (the lactose permease that imports it) and *lacA* — behind a promoter and an *operator*, a short sequence overlapping the promoter. A separate [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene), *lacI*, makes the *lac repressor*, a [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) that binds the operator and blocks the polymerase. Lactose, converted in the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) to allolactose, is the *inducer*: it binds the repressor, changes its shape, and makes it let go of the operator. The operon is thus off unless lactose is present — *negative control* lifted by *induction*.

![The lac operon. Without lactose the repressor sits on the operator and the polymerase cannot start; with lactose the inducer pulls the repressor off and the three genes are transcribed into one messenger.](https://one-course.com/images/onecourse/chapters/biology-3/b1-expression-control/fig-44454560b7dd.svg)

*The [lac operon](#def-b1-expression-control-operon). Without lactose the [repressor](#def-b1-expression-control-operon) sits on the operator and the polymerase cannot start; with lactose the inducer pulls the [repressor](#def-b1-expression-control-operon) off and the three [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) are transcribed into one messenger.*

**Proposition 20.4 (The operon model).**

The lac [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) are controlled by a diffusible [repressor](#def-b1-expression-control-operon) acting on a site adjacent to the [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene): control is negative, the [repressor](#def-b1-expression-control-operon) acts in *trans* (from anywhere in the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)), and the operator acts in *cis* (only on the [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) next to it).

**Evidence.** Jacob and Monod (1959–1961) reasoned from mutants. Strains mutant in *lacI* ($I^-$) made the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) with or without lactose (*constitutive*); a normal *lacI* [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) introduced on a second copy of the region restored regulation, so the [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene)’s product is a diffusible [repressor](#def-b1-expression-control-operon) that a mutant lacks. Strains mutant in the operator ($O^c$) were also constitutive, but a second normal operator on another copy did not restore regulation — the operator only controls the [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) physically attached to it, so it is a site, not a product. A third class ($I^s$) could not be induced at all, and was dominant: a [repressor](#def-b1-expression-control-operon) that no longer binds the inducer. In the PaJaMo experiment (1959) a normal *lacI* [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) transferred by conjugation into an $I^-$ [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) shut off the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) synthesis within minutes: the [repressor](#def-b1-expression-control-operon) acts fast, and on transcription — the messenger was later shown to have a half-life of minutes. ∎

**Definition 20.5 (Positive control: CAP and cAMP).**

The lac promoter is weak: even without the [repressor](#def-b1-expression-control-operon), the polymerase starts rarely unless a second [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide), *CAP* (catabolite activator [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide)), is bound just upstream of it, bending the [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) and holding the polymerase in place. CAP binds [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) only when carrying *cyclic AMP*, whose level in the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) falls when glucose is abundant. The [operon](#def-b1-expression-control-operon) is therefore fully on only when lactose is present *and* glucose is absent: two signals, one negative and one positive, are integrated at one promoter. Given both sugars, *E. coli* eats the glucose first, pauses while cAMP rises and the lac [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) are made, then eats the lactose — the two-phase growth curve called *diauxie*, which Monod described in 1941 and which set him on the road to the [operon](#def-b1-expression-control-operon).

![Diauxic growth of E. coli on glucose plus lactose. The culture grows on glucose alone, stops when it runs out, and resumes on lactose after the half-hour it takes to induce the lac operon.](https://one-course.com/images/onecourse/chapters/biology-3/b1-expression-control/fig-0949ebd4a579.svg)

*Diauxic growth of *E. coli* on glucose plus lactose. The culture grows on glucose alone, stops when it runs out, and resumes on lactose after the half-hour it takes to induce the [lac operon](#def-b1-expression-control-operon).*

![The lac operon made visible: colonies on a plate containing X-gal, a colourless substrate that -galactosidase turns blue. Blue colonies express lacZ; white ones carry a broken gene — the reporter used in a thousand experiments.](https://one-course.com/images/onecourse/chapters/biology-3/b1-expression-control/img-27d15b010166.jpg)

*The [lac operon](#def-b1-expression-control-operon) made visible: colonies on a plate containing X-gal, a colourless substrate that $\beta$-galactosidase turns blue. Blue colonies express *lacZ*; white ones carry a broken [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) — the reporter used in a thousand experiments.*

**Method 20.6 (Predicting a lac phenotype).**

1. Write the genotype of each copy of the region: $I$ , $P$ , $O$ , $Z$ ( $^+$ normal, $^-$ inactive, $O^c$ operator-constitutive, $I^s$ [super-repressor](#def-b1-expression-control-operon) ).
2. The [repressor](#def-b1-expression-control-operon) acts in trans: one $I^+$ anywhere represses every normal operator; $I^s$ represses whatever the inducer.
3. The operator and promoter act in cis: an $O^c$ frees only the $Z$ on its own [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) ; a $P^-$ silences only its own [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) .
4. Ask, with and without inducer, whether each $Z^+$ [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) is transcribed; the phenotype is inducible, constitutive or uninducible accordingly. Then add glucose: without cAMP–CAP, transcription is low whatever the [repressor](#def-b1-expression-control-operon) does.

**Example 20.7 (Two partial diploids).**

$I^-\,O^+\,Z^+ / I^+\,O^+\,Z^-$: the $I^+$ copy makes [repressor](#def-b1-expression-control-operon) that binds the $O^+$ next to $Z^+$; inducible — the mutation is complemented. $I^+\,O^c\,Z^+ / I^+\,O^+\,Z^-$: the only working $Z$ sits behind an operator the [repressor](#def-b1-expression-control-operon) cannot bind; constitutive — the normal operator on the other copy cannot help, since it controls only the broken $Z$.

## 20.3 Other bacterial strategies

**Proposition 20.8 (Repression, attenuation and sigma factors).**

[Operons](#def-b1-expression-control-operon) for biosynthesis are controlled in the opposite sense: the *[trp operon](#prop-b1-expression-control-trp)*, five [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) for making tryptophan, is transcribed unless tryptophan is present — the [amino acid](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-aminoacid) binds the trp [repressor](#def-b1-expression-control-operon) and *enables* it to bind the operator (a corepressor). A second, finer control, *attenuation*, uses the coupling of transcription and translation in bacteria: the start of the messenger encodes a short peptide with two tryptophans in a row; if tryptophan-loaded tRNA is abundant, a [ribosome](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#def-b1-gene-expression-ribosome) translates it quickly and the [RNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) behind folds into a terminator hairpin that stops the polymerase before the [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene); if tryptophan is scarce, the [ribosome](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#def-b1-gene-expression-ribosome) stalls at the tryptophan [codons](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#def-b1-gene-expression-code) and the [RNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) folds differently, letting transcription continue. Bacteria also switch whole sets of [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) by changing the $\sigma$ subunit of their polymerase: a heat-shock $\sigma$ directs it to the promoters of chaperone [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene); a sporulation $\sigma$ to those of spore formation.

## 20.4 Control in eukaryotes

**Definition 20.9 (Transcription factors, enhancers).**

In eukaryotes the polymerase never starts by itself: the general factors at the promoter ([Chapter 19](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#ch-b1-gene-expression)) recruit it, and the rate is set by *transcription factors* bound to *regulatory sequences* — some near the promoter, many in *enhancers* that can lie thousands of [base pairs](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#thm-b1-nucleic-acids-helix) away, upstream, downstream or in an [intron](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene), in either orientation, and act by *looping* the [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) so that the factors bound on them touch the promoter’s complex through mediator [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide). A transcription factor is modular: a *DNA-binding domain* that recognises a short sequence (helix-turn-helix, zinc finger, leucine zipper families) and an *activation* or *repression domain* that recruits or blocks the machinery. A [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) is read when the right *combination* of factors is present: a few hundred factors, in combinations, control twenty thousand [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene).

![Enhancer action. Activators bound to a distant enhancer are brought to the promoter by looping of the DNA, and a mediator complex relays their signal to the polymerase.](https://one-course.com/images/onecourse/chapters/biology-3/b1-expression-control/fig-460fb3570657.svg)

*[Enhancer](#def-b1-expression-control-enhancer) action. Activators bound to a distant [enhancer](#def-b1-expression-control-enhancer) are brought to the promoter by looping of the [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain), and a mediator complex relays their signal to the polymerase.*

**Proposition 20.10 (Chromatin is part of the control).**

A [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) wrapped in [nucleosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-nucleosome) packed into heterochromatin cannot be read: the factors cannot reach it. Activators recruit [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) that *acetylate* the [histones](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-nucleosome), loosening their grip on the [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) and marking the region as open; [repressors](#def-b1-expression-control-operon) recruit [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) that remove the acetyl groups and add marks that compact the chromatin. Methyl groups added to cytosines of a promoter silence it durably, and the marks are copied at replication, so that a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s pattern of open and closed [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) is inherited by its daughters — the memory by which a liver [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s daughters stay liver [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) (the Year 3 volume treats these *epigenetic* mechanisms in depth).

**Evidence.** In the giant polytene [chromosomes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) of fly larvae (a thousand copies of each [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) side by side, banded), [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) being transcribed appear as *puffs* where the chromatin has unfolded; the hormone ecdysone, which triggers moulting, makes a specific set of puffs appear within minutes and others hours later, in a fixed sequence — transcription seen directly, and switched by a signal. [Genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) moved by [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) rearrangement next to heterochromatin are silenced in some [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and not others, and the state is inherited by their daughters. ∎

![A polytene chromosome from a fly’s salivary gland: banded, with two puffs where the chromatin has opened for transcription. Puffs appear and disappear as genes are switched on and off.](https://one-course.com/images/onecourse/chapters/biology-3/b1-expression-control/img-fccaea43354d.jpg)

*A polytene [chromosome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) from a fly’s salivary gland: banded, with two puffs where the chromatin has opened for transcription. Puffs appear and disappear as [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) are switched on and off.*

**Example 20.11 (A signal becomes a pattern of expression).**

Cortisol enters a liver [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and binds its receptor, a [transcription factor](#def-b1-expression-control-enhancer) kept inactive in the [cytosol](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-organelle); the complex enters the nucleus, binds a fifteen-base sequence present near a hundred [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) — those of [gluconeogenesis](https://one-course.com/books/biology/3/en/chapter/16-biosyntheses-and-the-integrated-cell#def-b1-biosyntheses-integration-gluconeogenesis) among them ([Chapter 16](https://one-course.com/books/biology/3/en/chapter/16-biosyntheses-and-the-integrated-cell#ch-b1-biosyntheses-integration)) — and recruits acetylases and mediator: within an hour the [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) of glucose synthesis are being made. The same hormone in a lymphocyte, whose open chromatin exposes a different set of those sequences, switches on [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) that kill the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell). One signal, one receptor, two responses: the difference is which [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) were accessible.

## 20.5 After transcription, and the making of a body

**Proposition 20.12 (Control beyond the promoter).**

A [eukaryotic cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-prokeuk) also decides how a transcript is spliced (alternative splicing gives a muscle and a brain different [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) from one [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene)), whether it is exported, how long it lasts (half-lives from minutes for regulatory [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide)’ messages to days for haemoglobin’s, set by sequences in the untranslated regions that bind [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) and small regulatory [RNAs](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain)), and whether it is translated (iron-starved [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) block the translation of the ferritin message by a [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) bound to its $5'$ end, and release it when iron is present). The [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide), once made, is controlled by modification and degradation ([Chapter 13](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#ch-b1-enzymes)). Each later level is faster and more local than the one before, and more expensive: transcription decides what the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) can do, the later levels what it does now.

**Proposition 20.13 (Differential expression makes a body).**

Every [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) of a multicellular [organism](https://one-course.com/books/biology/3/en/chapter/1-the-organism-a-system-in-interaction-with-its-environment#def-b1-organism-environment-organism) carries the same [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome); the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) differ because they express different subsets of it. *Housekeeping* [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) — a few thousand for metabolism, the [ribosome](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#def-b1-gene-expression-ribosome), the [cytoskeleton](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-cytoskeleton) — are on in every [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell); the rest are switched on in some [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and off in others by the combinations of [transcription factors](#def-b1-expression-control-enhancer) each [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) carries and the chromatin states it has inherited. A red [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s precursor turns on globin and off nearly everything else; a [neuron](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-nervous) turns on its [channels](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-transporters) and never divides again. *Differentiation* is the acquisition of a stable pattern of expression, and *development* (the Year 2 volume) is the process by which signals between [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) set those patterns in the right places.

**Evidence.** A nucleus taken from a differentiated frog [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and put into an egg whose own nucleus has been removed can direct the development of a whole tadpole (Gurdon, 1962; recalled from the High School volume): the differentiated [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) had lost no [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene), only switched them off, and the egg’s [cytoplasm](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) reset the switches. The [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) of a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) type, separated on a gel, differ from another type’s; its messengers, once sequenced, are a subset of the [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) specific to it; and a handful of [transcription factors](#def-b1-expression-control-enhancer) introduced into a skin [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) can reprogram it into a stem [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) or a [neuron](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-nervous). ∎

**Example 20.14 (A gene read in two organs).**

The [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) for the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) that makes glucose from glucose-6-phosphate is expressed in the liver and the kidney and in no other [tissue](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-tissue): its promoter carries sites for factors present only there, and in other [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) its promoter is methylated and its chromatin closed. A muscle, which carries the [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) intact, cannot release glucose into the blood ([Chapter 16](https://one-course.com/books/biology/3/en/chapter/16-biosyntheses-and-the-integrated-cell#ch-b1-biosyntheses-integration)) — not for lack of the [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) but because the [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) is not read. The [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) is the same; the expression is the [organ](https://one-course.com/books/biology/3/en/chapter/2-functional-organization-of-a-mammal#def-b1-mammal-organization-organ).

## 20.6 Exercises

**Exercise 20.1 ★.**

Name the elements of the [lac operon](#def-b1-expression-control-operon) and give the state of the [operon](#def-b1-expression-control-operon) with and without lactose, with and without glucose.

**Solution of Exercise 20.1.**

*lacI* ([repressor](#def-b1-expression-control-operon) [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene)), promoter, operator, *lacZ*, *lacY*, *lacA*, and the CAP site. No lactose: off ([repressor](#def-b1-expression-control-operon) bound). Lactose, glucose present: barely on ([repressor](#def-b1-expression-control-operon) off, but no cAMP–CAP). Lactose, no glucose: fully on. Neither sugar: off.

**Exercise 20.2 ★.**

Explain the difference between a [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) product that acts in trans and a site that acts in cis, with one example of each from the [operon](#def-b1-expression-control-operon).

**Solution of Exercise 20.2.**

A product acting in trans is a diffusible molecule that can act on any copy of its target in the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell): the [repressor](#def-b1-expression-control-operon). A site acting in cis is a [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) sequence that affects only the [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) physically linked to it: the operator.

**Exercise 20.3 ★.**

From the [diauxie](#def-b1-expression-control-cap) figure, read the duration of the lag and the doubling times on each sugar.

**Solution of Exercise 20.3.**

Lag about $36\,\mathrm{min}$ (from $2\,\mathrm{h}$ to $2.6\,\mathrm{h}$); doubling $20\,\mathrm{min}$ on glucose, $30\,\mathrm{min}$ on lactose.

**Exercise 20.4 ★.**

Define [enhancer](#def-b1-expression-control-enhancer), [transcription factor](#def-b1-expression-control-enhancer) and housekeeping [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene).

**Solution of Exercise 20.4.**

[Enhancer](#def-b1-expression-control-enhancer): a regulatory sequence, often distant, that raises a [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene)’s transcription when factors bind it. [Transcription factor](#def-b1-expression-control-enhancer): a [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) with a DNA-binding domain and an activation or repression domain that regulates transcription. Housekeeping [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene): one expressed in every [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) at a steady level.

**Exercise 20.5 ★★.**

Give the phenotype (inducible, constitutive, uninducible) of: $I^-$; $O^c$; $I^s$; $I^-\,O^+\,Z^+ / I^+\,O^+\,Z^+$; $I^s\,O^+\,Z^+ /
I^+\,O^+\,Z^+$; $I^+\,O^c\,Z^- / I^+\,O^+\,Z^+$.

**Solution of Exercise 20.5.**

$I^-$: constitutive. $O^c$: constitutive. $I^s$: uninducible. $I^-/I^+$: inducible (the $I^+$ [repressor](#def-b1-expression-control-operon) acts in trans). $I^s/I^+$: uninducible ($I^s$ dominant). $I^+\,O^c\,Z^- / I^+\,O^+\,Z^+$: inducible — the only working $Z$ is behind a normal operator.

**Exercise 20.6 ★★.**

Compare the lac and [trp operons](#prop-b1-expression-control-trp): what the small molecule does to the [repressor](#def-b1-expression-control-operon) in each, and why the logic is opposite.

**Solution of Exercise 20.6.**

Lac: the sugar (inducer) binds the [repressor](#def-b1-expression-control-operon) and *releases* it from the operator — the [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) are made when their substrate is present. Trp: the [amino acid](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-aminoacid) (corepressor) binds the [repressor](#def-b1-expression-control-operon) and *enables* it to bind — the [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) are made when their product is absent. Catabolic pathways are switched on by their input, anabolic ones off by their output.

**Exercise 20.7 ★★.**

A mutant cannot make cAMP. Predict its growth on glucose, on lactose alone, and on both, and the level of $\beta$-galactosidase in each case.

**Solution of Exercise 20.7.**

On glucose: normal growth (glucose needs no CAP). On lactose alone: almost no growth — without cAMP, CAP cannot activate the lac promoter, so the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) stays at a few percent of induced levels even with the [repressor](#def-b1-expression-control-operon) released. On both: growth on glucose, then a stop; no second phase. [Enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) low in every case.

**Exercise 20.8 ★★.**

Explain why attenuation is impossible in eukaryotes, from the architecture of the [eukaryotic cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-prokeuk).

**Solution of Exercise 20.8.**

Attenuation needs the [ribosome](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#def-b1-gene-expression-ribosome) to be translating the messenger while the polymerase is still transcribing it, so that the [ribosome](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#def-b1-gene-expression-ribosome)’s position shapes the [RNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain) behind the polymerase. In eukaryotes transcription is in the nucleus and translation in the [cytosol](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-organelle), and the message is not translated until it has been processed and exported.

**Exercise 20.9 ★★.**

An [enhancer](#def-b1-expression-control-enhancer) is moved from $5\,\mathrm{kb}$ upstream of its [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) to $5\,\mathrm{kb}$ downstream and inverted; the [gene](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) is still expressed. Explain what this shows about how [enhancers](#def-b1-expression-control-enhancer) work.

**Solution of Exercise 20.9.**

[Enhancers](#def-b1-expression-control-enhancer) act at a distance, in either orientation and on either side, so they cannot work by being read or by positioning the polymerase directly; they work by binding factors that contact the promoter through a loop of [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain), for which distance and orientation matter little.

**Exercise 20.10 ★★★.**

Five thousand $\beta$-galactosidase tetramers of $4096\,$ residues cost how many [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) (four per residue)? A [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s budget per generation is about $1 \times 10^{10}\,$ [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp). Compute the growth disadvantage of a constitutive mutant, and the number of generations for its share of a mixed population to fall from a half to a hundredth.

**Solution of Exercise 20.10.**

$5000\times 4096\times 4 = 8.2 \times 10^{7}$ [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp): $0.8\,\%$ of the budget. Growth rate lower by $0.8\,\%$: per generation the mutant’s share falls by the factor $2^{-0.008} = 0.9945$. From $1:1$ to $1:99$: $0.9945^n = 1/99$, $n = \ln 99/0.00555 = 830$ generations — a few weeks of continuous culture.

**Exercise 20.11 ★★★.**

A liver [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and a [neuron](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-nervous) of the same person are compared: same [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome), different [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide), and each division of the liver [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) gives liver [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell). Explain, with chromatin, factors and inheritance of marks, how the difference is made and how it is maintained.

**Solution of Exercise 20.11.**

Each [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) type carries a specific set of [transcription factors](#def-b1-expression-control-enhancer), which bind the [enhancers](#def-b1-expression-control-enhancer) of its [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) and recruit acetylases that open their chromatin, while the [genes](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-gene) of other types are methylated and packed into heterochromatin that no factor can reach. The factors maintain one another’s expression (a network with stable states), and the chromatin marks are copied at replication, so daughters inherit both the factors and the open and closed regions. The [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) is the same; the accessible [genome](https://one-course.com/books/biology/3/en/chapter/17-genomes-of-cells-and-viruses#def-b1-genomes-genome) is not, and the inaccessibility is inherited.

**Exercise 20.12 ★★★.**

“A bacterium reads its environment; a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) of a body reads its history.” Discuss in a paragraph the two kinds of control, their signals, their timescales and their reversibility.

**Solution of Exercise 20.12.**

A bacterium’s controls are tuned to the medium: a sugar, an [amino acid](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-aminoacid), a temperature binds a [repressor](#def-b1-expression-control-operon) or a [sigma factor](#prop-b1-expression-control-trp) and the response is complete in minutes and reversed as soon as the signal goes — expression tracks the environment. A body’s [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) answers to signals too, but its main decisions were taken during development and locked in chromatin: what it can express was set by the factors it inherited and the marks on its [DNA](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-chain), changed only by division and mostly irreversible. The bacterium is a reader of the present; the differentiated [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) has a memory that is its identity.

## 20.7 Problem: Diauxie

**Problem 20.1.**

Weekend problem — Monod’s two-phase growth curve reconstructed cell by cell: glucose exhausted, lactose induced, enzymes counted, mutants predicted and the cost of regulation reckoned, ending on the induction factor of $\beta$-galactosidase

A culture of *E. coli* starts at $10^7$ [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) per millilitre in a medium with $0.5\,\mathrm{mmol}/\mathrm{L}$ of glucose and $1.0\,\mathrm{mmol}/\mathrm{L}$ of lactose. On glucose the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) double every $20\,\mathrm{min}$, on lactose every $30\,\mathrm{min}$; a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) needs $1.5 \times 10^{-12}\,\mathrm{g}$ of sugar per division ($180\,\mathrm{g}/\mathrm{mol}$ of glucose; lactose, $342\,\mathrm{g}/\mathrm{mol}$, counts as two glucoses). Uninduced [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) hold 5 molecules of $\beta$-galactosidase; fully induced, $5000$. Induction takes $30\,\mathrm{min}$. The [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) is a tetramer of $4\times 1024$ residues; each residue costs 4 [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp); a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) budget is $10^{10}$ per division and its [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) $1.5 \times 10^{-13}\,\mathrm{g}$ ($110\,\mathrm{Da}$ per residue).

**Part I — The glucose phase.**

1. Compute the glucose available per millilitre, in grams.
2. How many divisions per millilitre can it support?
3. Starting from $10^7$ [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) , how many [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) are there when the glucose runs out? (A division makes one new [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) .)
4. How many doublings is that, and how long does the glucose phase last?
5. During this phase, what is the state of the [lac operon](#def-b1-expression-control-operon) , and why, in molecular terms ( [repressor](#def-b1-expression-control-operon) and CAP)?

**Part II — The switch.**

6. When the glucose is gone, what rises inside the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and what does it bind?
7. Lactose was present all along. Why was the [operon](#def-b1-expression-control-operon) nevertheless almost off during the glucose phase?
8. During the $30\,\mathrm{min}$ lag each [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) makes its $5000$ [enzymes](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) . Compute the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) molecules made per second per [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) , and the residues per second.
9. A [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) holds $20\,000$ [ribosomes](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#def-b1-gene-expression-ribosome) at $20\,$ residues per second. What fraction of its translation is devoted to $\beta$ -galactosidase during the lag?
10. Compute the mass of $5000$ tetramers and the fraction of the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ’s [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) they represent.
11. Compute the induction factor.
12. Why is the permease ( *lacY* ) as necessary as the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) for growth on lactose, and what happens to a *lacY* $^-$ mutant given lactose?

**Part III — The lactose phase.**

13. Compute the lactose available per millilitre in glucose equivalents, in grams.
14. How many further divisions does it support, and what is the final [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) count?
15. How long does the lactose phase last?
16. Draw up the timeline: glucose phase, lag, lactose phase, total.
17. Explain why the doubling time is longer on lactose (two reasons: one about the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) step, one about the permease).

**Part IV — Mutants and costs.**

18. An $I^-$ mutant: describe its growth curve on the same medium and its [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) level throughout.
19. A CAP $^-$ mutant: describe its curve and [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) level.
20. An $O^c$ mutant in a medium with lactose only: any difference from wild type? And with glucose only?
21. Compute the [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) cost per generation of making $5000$ tetramers, and the fraction of the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ’s budget.
22. If that fraction lengthens the generation time by the same fraction, by how much does the $I^-$ mutant’s growth rate lag the wild type’s on glucose?
23. Starting at equal numbers, after how many generations on glucose is the mutant one tenth of the population? ( $r^n =  0.1/0.9$ with $r$ the ratio of growth rates per generation, i.e. $2^{-\delta}$ for a lag $\delta$ in doublings.)
24. Explain why, nevertheless, $I^-$ mutants are common in laboratory strains grown on lactose.
25. State the result: the induction factor of $\beta$ -galactosidase, the cost of making it unnecessarily as a fraction of the [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) budget, and the total time of the diauxic experiment.

**Solution of Problem 20.1.**

**1.** $0.5\times 10^{-3}\times 180 = 0.09\,\mathrm{g}/\mathrm{L} =
9 \times 10^{-5}\,\mathrm{g}/\mathrm{mL}$. **2.** $9\times 10^{-5}/1.5\times 10^{-12} = 6 \times 10^{7}$ divisions. **3.** $10^7 + 6 \times 10^{7} = 7 \times 10^{7}$ [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) per mL. **4.** $7 = 2^n$: $n = 2.8$ doublings, $56\,\mathrm{min}$. **5.** Off: lactose (allolactose) has released the [repressor](#def-b1-expression-control-operon), but glucose keeps cAMP low, so CAP is not bound and the promoter is nearly silent; also the permease is scarce, so little lactose enters. **6.** cAMP rises and binds CAP, which binds the promoter. **7.** Negative control was lifted but positive control was absent: a weak promoter without CAP starts rarely ([catabolite repression](#def-b1-expression-control-cap)). **8.** $5000/1800 = 2.8$ tetramers per second; $2.8\times 4096 =
11\,400$ residues per second. **9.** Capacity $20\,000\times 20 = 4 \times 10^{5}$ residues per second: $3\,\%$ of the [ribosomes](https://one-course.com/books/biology/3/en/chapter/19-gene-expression-transcription-and-translation#def-b1-gene-expression-ribosome). **10.** $5000\times 4096\times 110\times 1.66\times 10^{-24} =
3.7 \times 10^{-15}\,\mathrm{g}$: $2.5\,\%$ of the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide). **11.** $5000/5 = 1000$. **12.** Lactose cannot cross the membrane without the permease; a *lacY*$^-$ mutant has the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) but no substrate inside and does not grow on lactose (nor induce well, since the inducer is made from lactose inside the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)). **13.** $1.0\times 10^{-3}\times 342 = 0.342\,\mathrm{g}/\mathrm{L}$, worth $2\times 180 = 360\,\mathrm{g}$ of glucose per mole, i.e. $0.36\,\mathrm{g}/\mathrm{L}$ $= 3.6 \times 10^{-4}\,\mathrm{g}/\mathrm{mL}$. **14.** $3.6\times 10^{-4}/1.5\times 10^{-12} = 2.4 \times 10^{8}$ divisions; final $7 \times 10^{7} + 2.4 \times 10^{8} = 3.1 \times 10^{8}$ per mL. **15.** $3.1/0.7 = 4.4 = 2^n$: $n = 2.1$ doublings, $64\,\mathrm{min}$. **16.** Glucose $56\,\mathrm{min}$, lag $30\,\mathrm{min}$, lactose $64\,\mathrm{min}$: $150\,\mathrm{min}$ in all. **17.** Lactose must first be hydrolysed, an extra enzymatic step whose rate limits the supply of glucose; and the permease uses the proton gradient to import it, a cost glucose transport does not pay. **18.** $I^-$: [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) at $5000$ throughout (constitutive, once glucose is gone; on glucose CAP still limits it, so the level is intermediate); its lag is shorter or absent, so the curve shows a smaller pause; the cost slows it slightly on glucose. **19.** CAP$^-$: grows on glucose to $7 \times 10^{7}$, then stops: the [lac operon](#def-b1-expression-control-operon) cannot be activated, the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) stays near 5 molecules, and the lactose is never used. **20.** On lactose only: none in [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) level once induced (both fully on) and essentially none in growth; $O^c$ merely lacks the delay of induction. On glucose only: $O^c$ makes the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) uselessly (as far as CAP allows), wild type does not. **21.** $5000\times 4096\times 4 = 8.2 \times 10^{7}$ [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp): $0.8\,\%$ of $10^{10}$. **22.** Generation time longer by $0.8\,\%$: growth rate lower by $0.8\,\%$, $\delta = 0.008$ doublings per generation. **23.** $r = 2^{-0.008} = 0.99447$; $r^n = 0.111$: $n =
\ln 0.111/\ln 0.99447 = 2.20/0.00555 = 400$ generations. **24.** On lactose the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme) is needed anyway, so the mutant pays nothing and gains the lag: it is not selected against and is sometimes selected for; and laboratory strains are grown for convenience, not competition. **25.** Induction factor 1000 (5 to $5000$ molecules); unnecessary synthesis costs $0.8\,\%$ of the [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) budget; the experiment lasts about two and a half hours.